Applicable Differential Geometry (London Mathematical Society Lecture Note Series) (Paperback)

~ (Author), F. A. E. Pirani (Author) "The reader of this book is assumed to have a working knowledge of vector calculus..." (more)
Key Phrases: affine metric space, special frame field, infinitesimal affine transformation (more...)

Editorial Reviews

Product Description

This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.

Book Description

Manifolds, metrics, connections, Lie groups, spinors and bundles are among the geometrical topics useful in mathematics and theoretical physics that are included in this introduction.

Product Details

• Paperback: 404 pages
• Publisher: Cambridge University Press (April 24, 1987)
• Language: English
• ISBN-10: 0521231906
• ISBN-13: 978-0521231909
• Product Dimensions: 8.9 x 6 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #2,247,894 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

5.0 out of 5 stars Highly recommended textbook, November 15, 2007

By	Marian Fecko (Comenius University, Bratislava, Slovakia) - See all my reviews (REAL NAME)

I think the book by Crampin and Pirani may serve as an example of a thoughtfully written and useful textbook.
It treats those parts of differential geometry which are important in application (as the title indicates), especially in physics and related subjects.
It is written in a clear and comprehensible style and may also be used by beginners not being exposed to lectures on the subject.
Perhaps it should be mentioned that the book does not contain integration theory of forms.
However, I do not regard this as a substantial drawback, there are many standard sources (Flanders, Spivak, ...) to fill this gap after becoming familiar with the rich stuff which IS there.
(No book on the subject gives you all you might want and the one under consideration gives you quite a lot.)